Numerical Study on Proppant Transport in Hydraulic Fractures Using a Pseudo-3D Model for Multilayered Reservoirs

SPE Journal ◽  
2021 ◽  
pp. 1-16
Author(s):  
Xi Zhang ◽  
Lifeng Yang ◽  
Dingwei Weng ◽  
Zhen Wang ◽  
Robert G. Jeffrey
Keyword(s):  
Hydraulic Fracture ◽  
Transport Model ◽  
Numerical Study ◽  
Soft Rock ◽  
Injection Pressure ◽  
Field Measurements ◽  
Fracture Plane ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Proppant Transport

Summary In this paper, we incorporated a kinematic proppant transport model for spherical suspensions in hydraulic fractures developed by Dontsov and Peirce (2014) in a pseudo-3D hydraulic-fracture simulator for multilayered rocks to capture a different proppant transport speed than fluid flow and abridged fracture channel by highly concentrated suspensions. For pressure-driven proppant transport, the bridges made of compact proppant particles can lead to both proppant distribution discontinuity and increased fracture aperture and height because of the higher pressure. The model is applied to growth of a fracture from a vertical well, which can contain thin-bedded intervals and more than one opened hydraulic-fracture interval, because the fracture plane extends in height through layers with contrasts in stress and material properties. Three numerical examples demonstrate that a loss of vertical connectivity can occur among multiple fracture sections, and proppant particles are transported along the more compliant layers. The proppant migration within a narrow fracture in a thin soft rock layer can result in bridging and formation of a proppant plug that strongly limits fluid speed. This generates an increase of injection pressure associated with fracture screenout, and these screenout events can emerge at different places along the fracture. Next, because of the lack of pretreatment geomechanical data, the values of layer stress and leakoff coefficient are adjusted for a field case so that the varying bottomhole pressure and fracture length are in line with the field measurements. This paper provides a useful illustration for hydraulic-fracturing treatments with proppant transport affected by and interacting with reservoir lithological complexities.

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in Three-Dimensional Discrete Fracture Networks

2015 ◽  
Author(s):  
Mark W. McClure ◽  
Mohsen Babazadeh ◽  
Sogo Shiozawa ◽  
Jian Huang
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Three Dimensional ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Field Scale ◽  
Discrete Fracture Networks ◽  
Discrete Fracture

Abstract We developed a hydraulic fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, three-dimensional discrete fracture networks. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical relations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical one-dimensional leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is treated with linear elastic fracture mechanics. Non-Darcy pressure drop in the fractures due to high flow rate is simulated using Forchheimer's equation. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic fracture height containment as a model assumption. The code is efficient enough to perform field-scale simulations of hydraulic fracturing with a discrete fracture network containing thousands of fractures, using only a single compute node. Limitations of the model are that all fractures must be vertical, the mechanical calculations assume a linearly elastic and homogeneous medium, proppant transport is not included, and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low permeability formations, and which are not predicted by classical hydraulic fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.

Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1302-1320 ◽  
Author(s):  
Mark W. McClure ◽  
Mohsen Babazadeh ◽  
Sogo Shiozawa ◽  
Jian Huang
Keyword(s):  
Hydraulic Fracturing ◽  
Hydraulic Fracture ◽  
Fluid Pressure ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Natural Fractures ◽  
Fracture Networks ◽  
Field Scale ◽  
Discrete Fracture Networks ◽  
Discrete Fracture

Summary We developed a hydraulic-fracturing simulator that implicitly couples fluid flow with the stresses induced by fracture deformation in large, complex, 3D discrete-fracture networks (DFNs). The code is efficient enough to perform field-scale simulations of hydraulic fracturing in DFNs containing thousands of fractures, without relying on distributed-memory parallelization. The simulator can describe propagation of hydraulic fractures and opening and shear stimulation of natural fractures. Fracture elements can open or slide, depending on their stress state, fluid pressure, and mechanical properties. Fracture sliding occurs in the direction of maximum resolved shear stress. Nonlinear empirical equations are used to relate normal stress, fracture opening, and fracture sliding to fracture aperture and transmissivity. Fluid leakoff is treated with a semianalytical 1D leakoff model that accounts for changing pressure in the fracture over time. Fracture propagation is modeled with linear-elastic fracture mechanics. The Forchheimer equation (Forchheimer 1901) is used to simulate non-Darcy pressure drop in the fractures because of high flow rate. A crossing criterion is implemented that predicts whether propagating hydraulic fractures will cross natural fractures or terminate against them, depending on orientation and stress anisotropy. Height containment of propagating hydraulic fractures between bedding layers can be modeled with a vertically heterogeneous stress field or by explicitly imposing hydraulic-fracture-height containment as a model assumption. Limitations of the model are that all fractures must be vertical; the mechanical calculations assume a linearly elastic and homogeneous medium; proppant transport is not included; and the locations of potentially forming hydraulic fractures must be specified in advance. Simulations were performed of a single propagating hydraulic fracture with and without leakoff to validate the code against classical analytical solutions. Field-scale simulations were performed of hydraulic fracturing in a densely naturally fractured formation. The simulations demonstrate how interaction with natural fractures in the formation can help explain the high net pressures, relatively short fracture lengths, and broad regions of microseismicity that are often observed in the field during stimulation in low-permeability formations, and that are not predicted by classical hydraulic-fracturing models. Depending on input parameters, our simulations predicted a variety of stimulation behaviors, from long hydraulic fractures with minimal leakoff into surrounding fractures to broad regions of dense fracturing with a branching network of many natural and newly formed fractures.

A Novel Conceptual Model for the Flow and Transport in Fractured Rock

1990 ◽  
Vol 212 ◽  
Author(s):  
V. Taivassalo ◽  
A. Hautojärvi
Keyword(s):  
Field Experiments ◽  
Molecular Diffusion ◽  
Transport Model ◽  
Fractured Rock ◽  
Tracer Tests ◽  
Crystalline Rock ◽  
Research Area ◽  
Fracture Plane ◽  
Fracture Aperture ◽  
Test Case

ABSTRACTIn crystalline rock groundwater flows predominantly in fractures and fissures. Strongly varying fracture aperture guides the flow preferentially in some parts of a fracture plane, in so called channels. In our hydraulic model the degree of channeling together with the aperture variation along a channel is included as a factor which is the ratio of the aperture from transmissivity measurements and the aperture from the tracer tests.The developed transport model takes into account the coupling of molecular diffusion and advection in a velocity field varying linearly over a characteristic width. Various flow velocities in different parts of a channel cause a transient phase with non-Fickian behavior of dispersion. This might erroneously be attributed to other processes e.g. matrix diffusion when not taken into account in the migration modeling of tracers. Molecular diffusion across the flow field, however, tends to smooth out the transport time differences. With time the dispersion diminishes and becomes more symmetric in confined channels.The concept and models have been applied to predict and interpret field experiments aimed to investigate transport over long distances in highly conductive fracture zones. The analyzed experiments have been performed at the Finnsjön research area in Sweden and they belong to the test case 5 of the INTRAVAL project.

scholarly journals Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures

2014 ◽  
Vol 760 ◽  
pp. 567-590 ◽  
Author(s):  
E. V. Dontsov ◽  
A. P. Peirce
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Hydraulic Fracturing ◽  
Transport Model ◽  
Fluid Velocity ◽  
Spherical Particles ◽  
Hydraulic Fractures ◽  
Gravitational Settling ◽  
Proppant Transport ◽  
Two Dimensional Flow

AbstractThe goal of this study is to analyse the steady flow of a Newtonian fluid mixed with spherical particles in a channel for the purpose of modelling proppant transport with gravitational settling in hydraulic fractures. The developments are based on a continuum constitutive model for a slurry, which is approximated by an empirical formula. It is shown that the problem under consideration features a two-dimensional flow and a boundary layer, which effectively introduces slip at the boundary and allows us to describe a transition from Poiseuille flow to Darcy’s law for high proppant concentrations. The expressions for both the outer (i.e. outside the boundary layer) and inner (i.e. within the boundary layer) solutions are obtained in terms of the particle concentration, particle velocity and fluid velocity. Unfortunately, these solutions require the numerical solution of an integral equation, and, as a result, the development of a proppant transport model for hydraulic fracturing based on these results is not practicable. To reduce the complexity of the problem, an approximate solution is introduced. To validate the use of this approximation, the error is estimated for different regimes of flow. The approximate solution is then used to calculate the expressions for the slurry flux and the proppant flux, which are the basis for a model that can be used to account for proppant transport with gravitational settling in a fully coupled hydraulic fracturing simulator.

Modeling of Proppant Distribution During Fracturing of Multiple Perforation Clusters in Horizontal Wells

2021 ◽  
Author(s):  
Konstantin Sinkov ◽  
Xiaowei Weng ◽  
Olga Kresse
Keyword(s):  
Transport Model ◽  
Dynamic Pressure ◽  
Formation Rate ◽  
Network Models ◽  
Fracture Network ◽  
Low Flow ◽  
Hydraulic Fractures ◽  
Fluid Viscosity ◽  
Pumping Rate ◽  
Proppant Transport

Abstract Uniformity of proppant distribution among multiple perforation clusters affects treatment efficiency in multistage fractured wells stimulated using the plug-and-perf technique. Multiple physical phenomena taking place in the well and perforation tunnels can cause uneven proppant distribution among multiple clusters. The problem has been studied in the recent years with experimental and computational fluid dynamics (CFD) methods, which provide useful insights but are impractical for routine designs. Simplified models that incorporated the proppant transport efficiency (PTE) correlation derived from the CFD results in a hydraulic fracture model have been also presented in literature. In this paper, we present a numerical model that simulates the transient proppant slurry flow in the wellbore, considering proppant transport and settling including bed formation, rate- and concentration-dependent pressure drop, PTE, and dynamic pressure coupling with the hydraulic fractures. The model is efficient and is designed to be an independent wellbore transport model so it can be integrated with any fracture models, including fully 3D and/or complex fracture network models, for practical design optimization. The model predictions are compared and found to agree with previously published studies. Parametric studies demonstrate sensitivity of proppant distribution to grain size, fluid viscosity, and pumping rate for fixed perforation designs. Analysis of the simulation results shows that the dominant cause of uneven proppant distribution is proppant inertia. Possible slurry stratification is less important, except for the cases with relatively low flow rates and near toe clusters. Accordingly, proppant distribution is less sensitive to perforation phasing than to the number of perforations in clusters. Alterations of the number of perforations per cluster within a stage enable achieving more even proppant distribution.

Intrinsic anisotropy in fracture permeability

2015 ◽  
Vol 3 (3) ◽  
pp. ST43-ST53 ◽  
Author(s):  
Mehdi Mokhtari ◽  
Azra N. Tutuncu ◽  
Gregory N. Boitnott
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Hydraulic Fracture ◽  
Numerical Data ◽  
Fracture Aperture ◽  
Fracture Permeability ◽  
Fracture Geometry ◽  
Mechanical Fracture ◽  
Proppant Transport ◽  
Intrinsic Anisotropy

Contrary to the assumption in cubic law, the surface of fractures has some degree of roughness, which impacts their fluid dynamics. Incorporating the effect of roughness can improve the simulation of fluid flow in fractures and faults, as well as proppant transport in hydraulic fracturing. To investigate the effect of roughness on the fluid flow, we created a fracture using the Brazilian test, and its roughness was measured using a laser profilometer. Experimental permeability measurements showed a reduction in permeability as the effective stress increased. However, the unmatching surfaces of the fracture prevented its complete mechanical closure. Numerical simulations of the fluid dynamics were conducted on the measured fracture geometry. We determined that the hydraulic fracture aperture is less than the mechanical fracture aperture and that there was anisotropy in the fracture permeability. The ratio of hydraulic fracture aperture to mechanical fracture aperture, as well as anisotropy in fracture permeability, increased when the fracture aperture decreased. The anisotropy in fracture permeability was 45% at the lowest simulated fracture aperture. Integrating the experimental and numerical data, we estimated the fracture porosity and fracture permeability.

Development of a New Mathematical Model To Quantitatively Evaluate Equilibrium Height of Proppant Bed in Hydraulic Fractures for Slickwater Treatment

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2158-2174 ◽  
Author(s):  
Xiaodong Hu ◽  
Kan Wu ◽  
Xianzhi Song ◽  
Wei Yu ◽  
Lihua Zuo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Critical Velocity ◽  
Hydraulic Fracture ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Proppant Transport ◽  
Fluid Properties ◽  
Equilibrium Height

Summary The proppant bed develops and its height grows until it reaches the critical velocity and equilibrium height. This paper proposes a comprehensive mathematical model to evaluate the equilibrium height for slickwater treatment. We use well-accepted published experimental data and models from other groups to validate our model. After that, we investigate the effects of proppant properties and fluid properties on the equilibrium height. This work can provide critical insights to optimize the design of proppant parameters in a hydraulic fracture. Meanwhile, this model can be incorporated into fracture-propagation simulators for simulating proppant transport.

Propagation, proppant transport and the evolution of transport properties of hydraulic fractures

2018 ◽  
Vol 855 ◽  
pp. 503-534 ◽  
Author(s):  
Jiehao Wang ◽  
Derek Elsworth ◽  
Martin K. Denison
Keyword(s):  
Preferential Flow ◽  
Fluid Pressure ◽  
Fracture Propagation ◽  
Hydraulic Fractures ◽  
Fracture Aperture ◽  
Fluid Viscosity ◽  
Fracture Conductivity ◽  
Proppant Transport ◽  
Fracture Closure ◽  
Proppant Embedment

Hydraulic fracturing is a widely used method for well stimulation to enhance hydrocarbon recovery. Permeability, or fluid conductivity, of the hydraulic fracture is a key parameter to determine the fluid production rate, and is principally conditioned by fracture geometry and the distribution of the encased proppant. A numerical model is developed to describe proppant transport within a propagating blade-shaped fracture towards defining the fracture conductivity and reservoir production after fracture closure. Fracture propagation is formulated based on the PKN-formalism coupled with advective transport of an equivalent slurry representing a proppant-laden fluid. Empirical constitutive relations are incorporated to define rheology of the slurry, proppant transport with bulk slurry flow, proppant gravitational settling, and finally the transition from Poiseuille (fracture) flow to Darcy (proppant pack) flow. At the maximum extent of the fluid-driven fracture, as driving pressure is released, a fracture closure model is employed to follow the evolution of fracture conductivity with the decreasing fluid pressure. This model is capable of accommodating the mechanical response of the proppant pack, fracture closure of potentially contacting rough surfaces, proppant embedment into fracture walls, and most importantly flexural displacement of the unsupported spans of the fracture. Results show that reduced fluid viscosity increases the length of the resulting fracture, while rapid leak-off decreases it, with both characteristics minimizing fracture width over converse conditions. Proppant density and size do not significantly influence fracture propagation. Proppant settling ensues throughout fracture advance, and is accelerated by a lower viscosity fluid or greater proppant density or size, resulting in accumulation of a proppant bed at the fracture base. ‘Screen-out’ of proppant at the fracture tip can occur where the fracture aperture is only several times the diameter of the individual proppant particles. After fracture closure, proppant packs comprising larger particles exhibit higher conductivity. More importantly, high-conductivity flow channels are necessarily formed around proppant banks due to the flexural displacement of the fracture walls, which offer preferential flow pathways and significantly influence the distribution of fluid transport. Higher compacting stresses are observed around the edge of proppant banks, resulting in greater depths of proppant embedment into the fracture walls and/or an increased potential for proppant crushing.

Numerical study of an electrode-based resistivity tool for fracture diagnostics in steel-cased wellbores

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. D41-D48 ◽  
Author(s):  
Peng Zhang ◽  
Yaniv Brick ◽  
Mukul M. Sharma
Keyword(s):  
Hydraulic Fracture ◽  
Numerical Study ◽  
Hydraulic Fractures ◽  
Coiled Tubing ◽  
Aspect Ratios ◽  
Before And After ◽  
Bottom Hole Assembly ◽  
Insulating Gap ◽  
Subsurface Fractures ◽  
Volume Method

The efficiency of a hydraulic fracture treatment depends primarily on the dimensions and orientation of propped fractures. We have developed a novel electrode-based resistivity tool concept for mapping proppant distribution in hydraulic fractures in steel-cased wellbores. The proposed tool configuration is shown to overcome the severe limitations of induction tools for the detection and resolution of propped fracture geometries in such wellbores. The concept makes use of an array of electrically insulating gap subsections, which are installed and cemented as permanent parts of the casing string, separating the casing sections. By imposing voltages on the insulating gaps, the conductive casing is excited directly, thus avoiding through-casing signal degradation caused by its high electrical conductivity. This allows us to detect subsurface fractures propped with conductive proppant. The envisioned measurements are performed by running a bottom-hole assembly into the fractured zone on a coiled tubing to impose a voltage across each insulating gap at a time, before and after hydraulic fracture operations. For each excited insulating gap, the voltages across all other insulating gaps are recorded by the electronics embedded in the insulating gaps. To interpret the envisioned measurements, a forward model of the tool, based on a finite volume method, is developed, and the design’s sensitivity to the fracture parameters is demonstrated via case studies. The results indicate that measurements made based on the proposed concept will be highly sensitive to a fracture’s location, size, and angle, and less sensitive to a fracture’s shape. Simulations also indicate that direct contact of the fracture with an excited casing section enables the differentiation of fractures of up to a 100 m radius. Fractures with angles greater than 30° or aspect ratios greater than two can also be distinguished from the ones orthogonal to the well or with an aspect ratio of one.

Numerical Simulation Study of Proppant Transport in Cross Fractures

2022 ◽  
Author(s):  
Cong Lu ◽  
Li Ma ◽  
Jianchun Guo
Keyword(s):  
Hydraulic Fracturing ◽  
Transport Model ◽  
Injection Rate ◽  
Natural Fracture ◽  
Hydraulic Fractures ◽  
Fluid Viscosity ◽  
Natural Fractures ◽  
Fracturing Fluid ◽  
Proppant Transport ◽  
Approach Angle

Abstract Hydraulic fracturing technology is an important means to stimulate unconventional reservoirs, and the placement morphology of proppant in cross fractures is a key factor affecting the effect of hydraulic fracturing. It is very important to study the proppant transport law in cross fractures. In order to study the proppant transportation law in cross fractures, based on the CFD-DEM method, a proppant transport model in cross fractures was established. From the two aspects of the flow field in the fractures and the morphology of the proppant dune, the influence of the natural fracture approach angle, the fracturing fluid viscosity and injection rate on the proppant transport is studied. Based on the principle of hydropower similarity, the conductivity of proppant dune under different conditions is quantitatively studied. The results show that the natural fracture approach angle affects the distribution of proppant and fracturing fluid in natural fractures, and further affects the proppant placement morphology in hydraulic fractures and natural fractures. When the fracturing fluid viscosity is low and the displacement is small, the proppant forms a "high and narrow" dune at the entrance of the fracture. With the increase of the fracturing fluid viscosity and injection rate, the proppant settles to form a "short and wide" placement morphology. Compared with the natural fracture approach angle, the fracturing fluid viscosity and injection rate have a more significant impact on the conductivity of proppant dune. This paper investigated the proppant transportation in cross fractures, and quantitatively analyzes the conductivity of proppant dunes with different placement morphology. The results of this study can provide theoretical guidance for the design of hydraulic fracturing.

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